Question

a triangle has sides with lengths of 23 kilometers, 30 kilometers, and 38 kilometers. is it a right triangle?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 23\), \(b=30\), \(c = 38\).
Calculate \(a^{2}+b^{2}\): \(23^{2}+30^{2}=529 + 900=1429\).
Calculate \(c^{2}\): \(38^{2}=1444\).

Step2: Compare the results

Since \(1429
eq1444\), i.e., \(a^{2}+b^{2}
eq c^{2}\).

Answer:

no